Solving Systems by Elimination

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system by elimination?

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It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

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What is the first step in solving a system of equations by elimination?

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Align the equations so that corresponding variables and constants are in the same columns.

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How do you eliminate a variable in a system of equations?

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You can multiply one or both equations by a number to make the coefficients of one variable equal, then add or subtract the equations.

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What is the solution to a system of equations?

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The point (x, y) where the two lines intersect, representing the values of the variables that satisfy both equations.

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What does it mean if a system of equations has no solution?

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It means the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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It means the equations represent the same line, so every point on the line is a solution.

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